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Deep Water Wave Speed Calculator

Enter the wavelength in metres.

How it is calculated

For a deep-water gravity wave the phase speed is c = √(g × L / 2π) and the period is T = √(2π × L / g) = L / c, with L the wavelength in metres and g = 9.80665 m/s². The speed comes out in metres per second and is also converted to km/h by multiplying by 3.6. Period is in seconds. Longer waves travel faster: speed grows with the square root of the wavelength.

The tool only needs the wavelength, which must be above zero. It does not ask for water depth, so it assumes the water is deep compared with the wave (roughly half a wavelength or more); in shallow water the real speed is lower. It also ignores surface tension, so it does not suit very short ripples, and the results are rounded to two decimals.

Worked example

Take a swell with a wavelength of 156 m. First g × L / 2π = 9.80665 × 156 / 6.2832 ≈ 243.5. The square root gives a phase speed of 15.60 m/s. Multiplying by 3.6 gives 56.17 km/h. The period is the wavelength divided by the speed: 156 / 15.60 = 10.00 s. So a wave with a 156 m wavelength has a period of 10 seconds, a crest passing a fixed point every 10 s.

Try this example →

Common mistakes

  • Entering the wave period instead of the wavelength. The only input is the distance between two crests in metres.
  • Entering the wavelength in feet or km. The formula uses g in m/s², so the length must be in metres.
  • Using it in shallow water, near the shore. The tool assumes deep water, and a real wave slows down as the depth gets small compared with its wavelength.
  • Confusing phase speed with the speed of the wave's energy. In deep water the energy moves at half the phase speed, so a group of waves arrives later than the single crest speed suggests.
  • Mixing up wave height and wavelength. Height does not appear in the formula at all.

About this calculator

For ocean or lake waves traveling in water deeper than about half their wavelength — the “deep water” regime — the seafloor has no effect on wave motion, and the wave’s phase speed depends only on gravity and wavelength: c = √(gL/2π), with the period following as T = L/c = √(2πL/g). This is the linear (Airy) wave theory result for gravity waves, the dominant restoring force at these scales (surface tension only matters for much shorter ripples).

Oceanographers and coastal engineers use this relationship to predict how swell generated far offshore will arrive at a coastline, and it’s the same physics behind surf forecasting models that translate open-ocean wavelength and period into expected wave speed. Naval architects also rely on it when estimating how a vessel’s wake or a storm swell’s energy will propagate — enter a wavelength in metres and the calculator returns both the phase speed and period.

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  • Editorial team

    Wave reports usually quote the period, not the wavelength. In deep water the wavelength is about 1.56 times the period squared in metres, so a 10 second swell is roughly 156 m long and moves at 15.60 m/s. That also tells you whether the deep-water assumption holds: the sea should be deeper than about half the wavelength, here around 78 m. What period are you starting from?

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